My uninformed opinion is that games should be a good medium for teaching young children. (I would be very interested in hearing opinions about this from people who actually work in education.) I think a surprising amount can be learned by carefully inspecting even a game as simple as Minesweeper. There are various "lemmas" you can prove in Minesweeper about how various configurations uniquely pin down the location of mines or non-mines and I suspect this could be an accessible introduction to mathematical proof (the advantage being that all of the relevant proofs can be done by analyzing a finite number of cases). I haven't actually tried this though.